A charged particle of mass `m` and charge `q` travels on a circular path of radius `r` that is perpendicular to a magnetic field `B`. The time takeen by the particle to complete one revolution is

Options

A. `(2pimq)/B`
B. `(2piq^(2)B)/m`
C. `(2piqB)/m`
D. `(2pim)/(qB)`

Answer

D

Explanation

Magnetic force `F=qvB [ :' theta=90^(@)]`…..i
Centripetal force `F=(mv^(2))/r`………….ii
Fromeqs I and ii we have
`(mv^(2))/r=qvB` or `r=(mv)/(qB)`
The time taken by the particle to complete one revolution,
`T=(2pir)/V=(2pim)/(vqB)=(2pim)/(qB)`